Study On Migration Dynamics And Time-varying Characteristics Of Cancer Cell In Complex Microenvironment

Cell migration,which is regulated by intracellular signaling pathways(ICSP)and extracellular matrix(ECM),plays an indispensable role in many physiological and pathological process such as normal tissue development and cancer metastasis.For example,the new Arpin protein inhibits the Arp2/3 complex and antagonizes an intrinsic positive feedback loop sustaining lamellipodial protrusion,decreasing the directional persistence of migration;the osteogenic differentiation of embryonic stem cells was facilitated on stiffer substrates,indicating that the mechanical signals greatly affect both early and terminal differentiation of embryonic stem cells.A lot of experiments and simulations concerning cell migration dynamics have been performed,but migration acceleration which is important for recognizing dynamics modes of cell migration and analyzing the regulation mechanisms of microenvironment in mechanical signal transmission,has not been systematically investigated.Thus,we firstly rigorously investigate and quantify the differences between persistent random walk and anisotropic persistent random walk models based on the analysis of cell migration trajectories and velocity auto-covariance function,both qualitatively and quantitatively.Secondly,we introduce the concepts of positive and negative anisotropy based on the motility parameters to study the effect of anisotropy on acceleration,especially the nonlinear and abnormal behaviors.We particularly elaborate and discuss the mechanisms and physical insights of abnormal behaviors in the case of positive anisotropy,focusing on the force exerted on migrating cells.Finally,we analyze two types of in vitro cell migration experiments and verify the universality of nonlinear and abnormal behaviors,and the consistence with numerical results.We conclude that the anisotropy of microenvironment is the cause of the nonlinear and abnormal dynamics,and the anisotropic persistent random walk can be as a suitable tool to analyze in vitro cell migration with different combinations of motility parameters.Our analysis provides new insights into the dynamics of cell migration in complex microenvironment,which also has implications in tissue engineering and cancer research.Moreover,there is a lack of rigorous and quantitative tools for analyzing the time-varying characteristics of cell migration in heterogeneous microenvironment,thus we develop a wavelet-based approach to derive the time-dependent motility parameters from cell migration trajectories,based on the time-varying persistent random walk model.We firstly apply the wavelet denoising and wavelet transform to obtain the wavelet power spectrum of migration velocities,and subsequently deriving the time-dependent motility parameters via Lorentzian power spectrum.Our results indicate the superiority of the method for estimating the intrinsic transient motility parameters,and robust against a variety of stochastic noises.Then we demonstrate the utility of our approach via analyzing experimental data of in vitro cell migration in distinct microenvironments,including the migration of MDA-MB-231 cells in confined micro-channel arrays and correlated migration of MCF-10 A cells due to ECM-mediated mechanical coupling.Our analysis shows that the approach can be as a powerful tool to accurately derive the time-dependent motility parameters,and further analyze the timedependent characteristics of cell migration regulated by complex microenvironment.In addition,Cell migration is typically modeled as a persistent random walk,which depends on two critical motility parameters,i.e.,persistence time and migration speed.It is generally very challenging to efficiently and accurately quantify the migration dynamics from noisy experimental data.Here,we firstly introduce the normalized Shannon entropy(SE)based on the Fourier power spectrum of cellular velocity to quantify migration dynamics.The Shannon entropy introduced here possesses the similar physical interpretation as the Gibbs entropy for thermal systems in that SE naturally reflects the degree of order or randomness of cellular migration,attaining the maximal value of unity for purely diffusive migration(i.e.,SE = 1 for the most“random” dynamics)and the minimal value of zero for purely ballistic dynamics(i.e.,SE = 0 for the most “ordered” dynamics).Then we introduce the time-varying Shannon entropy based on the wavelet power spectrum of cellular dynamics and demonstrate its superior utility to characterize the time-dependent persistence of cell migration,which is typically resulted from complex and time-varying intra or extracellular mechanisms.We finally apply the approach to analyze experimental data of in vitro cell migration regulated by distinct intracellular and extracellular mechanisms,exhibiting a rich spectrum of dynamic characteristics.Our analysis indicates that the Shannon entropy and wavelet transform(i.e.,SE-based approach)offers a simple and efficient framework to quantify cell migration dynamics in complex microenvironment.